The B.P of Dilcofenac is 412 deg C while that of Ciprofloxacin is 518.8 deg C. The maximum temperature for TG-1MS (ECD) and TG-5MS (FID) is 330 deg C. The maximum temperature for TG-1710MS is 280 deg C (FID and NPD).
If they are stable you can use GC. You don't need to heat the column up to boiling point of the analytes. Take a column with thin film like 0,1 or 0,25 um. TG1 or TG5. Run a temp. Program 50 (hold 2 minutes) ramp 10-15dwg.C/min to 280 or 300 (hold 20-30min). Check where you get a peak of the standard on the chromatogram. After that optimize the temp. prog. use splitless injection.
About temp. program -boiling point - retention relationship take a look on PAHs analysis by GC.
Thus, GC uses Hexane or Dichloromethane as solvents which are very non-polar while typical HPLC (reverse phase) solvents are Methanol, Acetonitrile, IPA, and Water.
Just because you have a hammer, does not mean everything is a nail. It is the molecule of interest that determines the technique of analysis (in either case of GC or HPLC you have to solubilize the molecule 1st).
In forensic toxicology analysis TG-5MS (ZB-5MS; HP-5MS) 30m; 0,25mm DIAM.; 0,25 um film thikness is typically used. However, for polar compounds peak shape can be poor. Thus You have to make derivatization.
For Dilcofenac and Ciprofloxacin You will obtain poor sensitivity using GC method. Derivatization will be required to obtain low LODs and LOQs. I don't know Your matrix, but it will be possible to analyse only e.g. pharmaceuticals without derivatization. In case when Your analytes are low volatile (as Yours) You should heat the column at 300 or even 310 dwg.C at the end of oven temperature program for longer time, as Grzegorz Boczkaj suggested, or use higer temperature program (e.g. 20-30dwg.C/min) to elute analytes from the column.